For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams (Q1359440)

Summary: We use Turaev's technique of shadows and gleams to parametrize the set of all knots in \(S^3\) with the same Hopf projection. We show that the Vassiliev invariants arising from the Jones polynomial \(J_t(K)\) are polynomials in the gleams, i.e., for \(n\geq 2\), then \(n\)-th order Vassiliev invariant \(u_n\), defined by \(J_{e^x}(K)= \sum_{n=0}^\infty u_n(K)x^n\), is a polynomial of degree \(2n\) in the gleams.